Expression of type ExprTuple

from the theory of proveit.numbers.division

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, m, n, w, x, y, z
from proveit.core_expr_types import w_1_to_m, z_1_to_n
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Complex, Mult, Neg, frac, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(w, sub_expr1)
sub_expr3 = IndexedVar(z, sub_expr1)
expr = ExprTuple(Lambda([w_1_to_m, x, y, z_1_to_n], Conditional(Equals(frac(x, Mult(w_1_to_m, Neg(y), z_1_to_n)), Neg(frac(x, Mult(w_1_to_m, y, z_1_to_n)))), And(ExprRange(sub_expr1, InSet(sub_expr2, Complex), one, m), InSet(x, Complex), InSet(y, Complex), ExprRange(sub_expr1, InSet(sub_expr3, Complex), one, n), NotEquals(y, zero), ExprRange(sub_expr1, NotEquals(sub_expr2, zero), one, m), ExprRange(sub_expr1, NotEquals(sub_expr3, zero), one, n)))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(w_{1}, w_{2}, \ldots, w_{m}, x, y, z_{1}, z_{2}, \ldots, z_{n}\right) \mapsto \left\{\frac{x}{w_{1} \cdot  w_{2} \cdot  \ldots \cdot  w_{m} \cdot \left(-y\right)\cdot z_{1} \cdot  z_{2} \cdot  \ldots \cdot  z_{n}} = \left(-\frac{x}{w_{1} \cdot  w_{2} \cdot  \ldots \cdot  w_{m} \cdot y\cdot z_{1} \cdot  z_{2} \cdot  \ldots \cdot  z_{n}}\right) \textrm{ if } \left(w_{1} \in \mathbb{C}\right) ,  \left(w_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(w_{m} \in \mathbb{C}\right) ,  x \in \mathbb{C} ,  y \in \mathbb{C}, \left(z_{1} \in \mathbb{C}\right) ,  \left(z_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(z_{n} \in \mathbb{C}\right) ,  y \neq 0, \left(w_{1} \neq 0\right) ,  \left(w_{2} \neq 0\right) ,  \ldots ,  \left(w_{m} \neq 0\right), \left(z_{1} \neq 0\right) ,  \left(z_{2} \neq 0\right) ,  \ldots ,  \left(z_{n} \neq 0\right)\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	52, 44, 53, 54
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14, 15, 16, 17, 18
10	Operation	operator: 35 operands: 19
11	Operation	operator: 48 operand: 29
12	ExprRange	lambda_map: 21 start_index: 58 end_index: 56
13	Operation	operator: 38 operands: 22
14	Operation	operator: 38 operands: 23
15	ExprRange	lambda_map: 24 start_index: 58 end_index: 59
16	Operation	operator: 41 operands: 25
17	ExprRange	lambda_map: 26 start_index: 58 end_index: 56
18	ExprRange	lambda_map: 27 start_index: 58 end_index: 59
19	ExprTuple	44, 28
20	ExprTuple	29
21	Lambda	parameter: 65 body: 30
22	ExprTuple	44, 46
23	ExprTuple	53, 46
24	Lambda	parameter: 65 body: 31
25	ExprTuple	53, 47
26	Lambda	parameter: 65 body: 32
27	Lambda	parameter: 65 body: 33
28	Operation	operator: 50 operands: 34
29	Operation	operator: 35 operands: 36
30	Operation	operator: 38 operands: 37
31	Operation	operator: 38 operands: 39
32	Operation	operator: 41 operands: 40
33	Operation	operator: 41 operands: 42
34	ExprTuple	52, 43, 54
35	Literal
36	ExprTuple	44, 45
37	ExprTuple	60, 46
38	Literal
39	ExprTuple	61, 46
40	ExprTuple	60, 47
41	Literal
42	ExprTuple	61, 47
43	Operation	operator: 48 operand: 53
44	Variable
45	Operation	operator: 50 operands: 51
46	Literal
47	Literal
48	Literal
49	ExprTuple	53
50	Literal
51	ExprTuple	52, 53, 54
52	ExprRange	lambda_map: 55 start_index: 58 end_index: 56
53	Variable
54	ExprRange	lambda_map: 57 start_index: 58 end_index: 59
55	Lambda	parameter: 65 body: 60
56	Variable
57	Lambda	parameter: 65 body: 61
58	Literal
59	Variable
60	IndexedVar	variable: 62 index: 65
61	IndexedVar	variable: 63 index: 65
62	Variable
63	Variable
64	ExprTuple	65
65	Variable